Isaac caused trouble at his private grade school, Westminster Christian, when growing up. "I set off a fire extinguisher in the gym, defaced a mural, just stupid stuff", he said in an interview.[16] He liked to make kids laugh. At one point, his teacher had to screen off his desk from the rest of the class with a piece of cardboard. Eventually, he was expelled.[17]

Isaac's entry into professional acting began at the Area Stage Company, Miami Beach, when Artistic Director John Rodaz cast him in a play.[18] He also acted in Miami-based City Theatre's Summer Shorts short play festival in 2000–2001. While in Miami, he played lead guitar and sang vocals for ska-punk band The Blinking Underdogs.[19] Other band members included Nick Speck (bass), Bill Sommer (drums), Alan Mills (trombone), Keith Cooper (saxophone), and Matt LaPlant (guitar).[20] The band enjoyed some success, opening for Green Day[21] and The Mighty Mighty Bosstones.[20] Isaac spent his musical years living a "straight edge" lifestyle.[22][23][24] Isaac put music to the side after being accepted into the acting program of New York's prestigious Juilliard School in 2001. While a student there, he worked on one of his first films, All About the Benjamins (2002). He was part of the Drama Division's Group 34 (2001–2005).[25]

In the current leading-man sea of buff, WASP-y dudes named Ryan and Chris, Isaac stands out. He's good-looking in a slightly imperfect manner that hearkens back to a pre-Ken-doll era of moviemaking: His nose is prominent, with a small dent at the tip. [...] "He has an interesting face," says Singer. "Like the great movie stars, like Harrison Ford, like Tom Cruise. [...] There's something about Oscar that could be Egyptian, Asiatic, Latino or Caucasian. His facial structure embodies a global human."

Isaac currently[when?] resides in Williamsburg, Brooklyn. He has been dubbed a sex symbol,[52][53] and "the internet's boyfriend" by multiple media outlets, most notably Rolling Stone magazine; of the label, Isaac stated, "[The Internet] never struck me as being into monogamous relationships. It's very promiscuous, the Internet."[12] Isaac married Danish film director Elvira Lind in February 2017.[54] Their son, Eugene,[55] was born in late April 2017.[56]

Isaac is an accomplished guitar player and singer and has been playing since he was 12. Speaking to Interview magazine, he stated, "I don't know if they were all functioning, but I did play in a bunch of bands. I was sort of a musical whore, so I played in industrial bands, hardcore bands, punk-ska bands—all sorts of bands." Isaac also said that he "played guitar and bass. I didn't do much vocals, although I did have one band where I was the lead singer. But that was when I was in college."[57]